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2022 PEA Q4

Production function: Y(L,K)=min⁡{2L,K}Y(L,K) = \min\{2L, K\}; cost C=wL+rKC = wL + rK, w,r>0w,r>0. Find (L∗,K∗)(L^*, K^*) minimizing cost subject to Y(L,K)≥YˉY(L,K) \geq \bar Y.

Reveal answer and solution

Answer

C

Solution

  1. 1

    With a Leontief technology, optimal input use sets the two arguments equal:

  2. 2
    2L=K=Yˉ⟹L∗=Yˉ2,  K∗=Yˉ. 2L = K = \bar Y \quad \Longrightarrow \quad L^* = \frac{\bar Y}{2},\ \ K^* = \bar Y.
  3. 3

    Hence option (C) is correct.

  4. 4

    \textit{Correction: The optimum is L∗=Yˉ/2L^* = \bar Y/2 and K∗=YˉK^* = \bar Y, which is option (C).}

Answer structure / marking notes

For min⁡{aL,bK}\min\{aL, bK\}, set aL=bK=YˉaL = bK = \bar Y and solve for inputs.

Content note

Imported from public/resources/isi/msqe/solutions/pea/2022/ISI_MSQE_PEA_2022_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.